Charles Counts

Math Problem to Solve?

A farmer had some ducks and cows in the field. He sent his children out to count the number of animals. Jean counted 50 heads. Charles counted 154 legs. How many of each kind were counted?

let d represent ducks, let c represent cows.

Assume that both ducks and cows have one head

d+c= 50

Assume that ducks have two feet while cows have 4 feet

2d +4c= 154

Isolate a variable in one of them:

d= 50 -c

sub this into the second equation:

2(50-c) + 4c= 154

100 -2c +4c=154

-2c +4c = 154 -100

2c = 54

c= 27

sub c= 27 into the equation above to find the number of ducks.

d= 50 -(27)

d= 50 -27

d= 23

Therefore there were 23 ducks and 27 cows.

NOTE: solved by substitution; the other guys did solving by elimination.

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